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MSVC_erfc.h
#ifndef OPENMM_MSVC_ERFC_H_
#define OPENMM_MSVC_ERFC_H_
/*
* Up to version 11 (VC++ 2012), Microsoft does not support the
* standard C99 erf() and erfc() functions so we have to fake them here.
* These were added in version 12 (VC++ 2013), which sets _MSC_VER=1800
* (VC11 has _MSC_VER=1700).
*/
#if defined(_MSC_VER)
#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950288
#endif
#if _MSC_VER <= 1700 // 1700 is VC11, 1800 is VC12
/***************************
* erf.cpp
* author: Steve Strand
* written: 29-Jan-04
***************************/
#include <cmath>
static const double rel_error= 1E-12; //calculate 12 significant figures
//you can adjust rel_error to trade off between accuracy and speed
//but don't ask for > 15 figures (assuming usual 52 bit mantissa in a double)
static double erfc(double x);
static double erf(double x)
//erf(x) = 2/sqrt(pi)*integral(exp(-t^2),t,0,x)
// = 2/sqrt(pi)*[x - x^3/3 + x^5/5*2! - x^7/7*3! + ...]
// = 1-erfc(x)
{
static const double two_sqrtpi= 1.128379167095512574; // 2/sqrt(pi)
if (fabs(x) > 2.2) {
return 1.0 - erfc(x); //use continued fraction when fabs(x) > 2.2
}
double sum= x, term= x, xsqr= x*x;
int j= 1;
do {
term*= xsqr/j;
sum-= term/(2*j+1);
++j;
term*= xsqr/j;
sum+= term/(2*j+1);
++j;
} while (fabs(term)/sum > rel_error);
return two_sqrtpi*sum;
}
static double erfc(double x)
//erfc(x) = 2/sqrt(pi)*integral(exp(-t^2),t,x,inf)
// = exp(-x^2)/sqrt(pi) * [1/x+ (1/2)/x+ (2/2)/x+ (3/2)/x+ (4/2)/x+ ...]
// = 1-erf(x)
//expression inside [] is a continued fraction so '+' means add to denominator only
{
static const double one_sqrtpi= 0.564189583547756287; // 1/sqrt(pi)
if (fabs(x) < 2.2) {
return 1.0 - erf(x); //use series when fabs(x) < 2.2
}
// Don't look for x==0 here!
if (x < 0) { //continued fraction only valid for x>0
return 2.0 - erfc(-x);
}
double a=1, b=x; //last two convergent numerators
double c=x, d=x*x+0.5; //last two convergent denominators
double q1, q2= b/d; //last two convergents (a/c and b/d)
double n= 1.0, t;
do {
t= a*n+b*x;
a= b;
b= t;
t= c*n+d*x;
c= d;
d= t;
n+= 0.5;
q1= q2;
q2= b/d;
} while (fabs(q1-q2)/q2 > rel_error);
return one_sqrtpi*exp(-x*x)*q2;
}
#endif // _MSC_VER <= 1700
#endif // _MSC_VER
#endif // OPENMM_MSVC_ERFC_H_